Opera makes one of the world's most widely used mobile phone internet browsers, and Mark Zuckerberg's social network is reportedly interested in the company as part of a plan to create a Facebook smartphone.

After surging by a quarter on the Oslo stock exchange, Opera shares fell back by midday but remained 17% higher than Friday's closing price at 40.1 Norwegian krone (NOK), valuing the firm at 4.8bn NOK (£510m).

The company declined to comment, while founder Jon von Tetzchner, who is the largest shareholder with 10.9%, said he was not aware of talks, according to Reuters.

Facebook has 350m mobile users a month, but has struggled to sell advertising on smartphone screens and is looking to extend its control over the mobile experience.

It is weeks away from launching its own phone apps store, which will promote and review services such as Pinterest and Spotify that incorporate Facebook links. Zuckerberg is understood to have recruited half a dozen iPhone engineers from Apple, and is said to be working with Taiwanese manufacturer HTC on a new handset.

"In our view, a bid for Opera makes strategic sense for Facebook, and we have previously discussed the possibilities for co-operation between the two companies," an analyst at Norwegian bank DNB said. "We expect that any successful bid would have to pay at least double the closing price from Friday. We have a buy recommendation on Opera with a price target of 60 NOK per share."

Doubling Friday's closing price would put an £860m price tag on the firm.

Opera creates browsers that allow desktop computers and phones to access the internet, and its software works with Apple and Microsoft machines. Although Opera's presence on desktop computers – where browsers from Apple, Microsoft, Google and Mozilla tend to dominate – is limited, it has been successful on cheap mobile phones.

The Opera Mini browser, which works on even simple handsets with small screens and limited memory, has been widely adopted in emerging markets and means 250 million people use an Opera product each month.